Open problem 2: Questions on the stability problem of periodic solutions in the \(N\)-body problem

DOI10.1007/s12346-015-0171-yzbMath1336.70029OpenAlexW1863805804MaRDI QIDQ904887

Long, Yiming

Publication date: 14 January 2016

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-015-0171-y

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10) Stability problems in rigid body dynamics (70E50)

Cites Work

• Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory
• Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem
• Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit
• Index theory for symplectic paths with applications
• An estimation for the hyperbolic region of elliptic Lagrangian solutions in the planar three-body problem
• Stability diagram for 4D linear periodic systems with applications to homographic solutions
• Analysis of the stability of a family of singular-limit linear periodic systems in \(\mathbb {R}^4\). Applications

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